Data update
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Ingy döt Net
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7735 changed files with 38060 additions and 199180 deletions
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with Ada.Containers.Indefinite_Ordered_Sets;
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with Ada.Finalization;
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with Ada.Text_IO; use Ada.Text_IO;
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procedure Heronian is
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package Int_IO is new Ada.Text_IO.Integer_IO(Integer);
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use Int_IO;
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-- ----- Some math...
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function GCD (A, B : in Natural) return Natural is (if B = 0 then A else GCD (B, A mod B));
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function Int_Sqrt (N : in Natural) return Natural is
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R1 : Natural := N;
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R2 : Natural;
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begin
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if N <= 1 then
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return N;
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end if;
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loop
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R2 := (R1+N/R1)/2;
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if R2 >= R1 then
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return R1;
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end if;
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R1 := R2;
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end loop;
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end Int_Sqrt;
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-- ----- Defines the triangle with sides as discriminants and a constructor which will
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-- compute its other characteristics
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type t_Triangle (A, B, C : Positive) is new Ada.Finalization.Controlled with record
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Is_Heronian : Boolean;
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Perimeter : Positive;
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Area : Natural;
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end record;
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overriding procedure Initialize (Self : in out t_Triangle) is
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-- Let's stick to integer computations, therefore a modified hero's formula
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-- will be used : S*(S-a)*(S-b)*(S-c) = (a+b+c)*(-a+b+c)*(a-b+c)*(a+b-c)/16
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-- This will require long integers because at max side size, the product
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-- before /16 excesses 2^31
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Long_Product : Long_Long_Integer;
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Short_Product : Natural;
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begin
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Self.Perimeter := Self.A + Self.B + Self.C;
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Long_Product := Long_Long_Integer(Self.Perimeter)
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* Long_Long_Integer(- Self.A + Self.B + Self.C)
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* Long_Long_Integer( Self.A - Self.B + Self.C)
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* Long_Long_Integer( Self.A + Self.B - Self.C);
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Short_Product := Natural(Long_Product / 16);
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Self.Area := Int_Sqrt (Short_Product);
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Self.Is_Heronian := (Long_Product mod 16 = 0) and (Self.Area * Self.Area = Short_Product);
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end Initialize;
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-- ----- Ordering triangles with criteria (Area,Perimeter,A,B,C)
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function "<" (Left, Right : in t_Triangle) return Boolean is
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(Left.Area < Right.Area or else (Left.Area = Right.Area and then
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(Left.Perimeter < Right.Perimeter or else (Left.Perimeter = Right.Perimeter and then
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(Left.A < Right.A or else (Left.A = Right.A and then
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(Left.B < Right.B or else (Left.B = Right.B and then
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Left.C < Right.C))))))));
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package Triangle_Lists is new Ada.Containers.Indefinite_Ordered_Sets (t_Triangle);
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use Triangle_Lists;
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-- ----- Displaying triangle characteristics
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Header : constant String := " A B C Per Area" & ASCII.LF & "---+---+---+---+-----";
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procedure Put_Triangle (Position : Cursor) is
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Triangle : constant t_Triangle := Element(Position);
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begin
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Put(Triangle.A, 3);
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Put(Triangle.B, 4);
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Put(Triangle.C, 4);
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Put(Triangle.Perimeter, 4);
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Put(Triangle.Area, 6);
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New_Line;
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end Put_Triangle;
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-- ----- Global variables
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Triangles : Set := Empty_Set;
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-- Instead of constructing two sets, or browsing all the beginning of the set during
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-- the second output, start/end cursors will be updated during the insertions.
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First_201 : Cursor := No_Element;
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Last_201 : Cursor := No_Element;
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procedure Memorize_Triangle (A, B, C : in Positive) is
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Candidate : t_Triangle(A, B, C);
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Position : Cursor;
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Dummy : Boolean;
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begin
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if Candidate.Is_Heronian then
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Triangles.Insert (Candidate, Position, Dummy);
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if Candidate.Area = 210 then
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First_201 := (if First_201 = No_Element then Position
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elsif Position < First_201 then Position
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else First_201);
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Last_201 := (if Last_201 = No_Element then Position
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elsif Last_201 < Position then Position
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else Last_201);
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end if;
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end if;
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end Memorize_Triangle;
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begin
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-- Loops restrict to unique A,B,C (ensured by A <= B <= C) with sides < 200 and for
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-- which a triangle is constructible : C is not greater than B+A (flat triangle)
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for A in 1..200 loop
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for B in A..200 loop
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for C in B..Integer'Min(A+B-1,200) loop
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-- Filter non-primitive triangles
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if GCD(GCD(A,B),C) = 1 then
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Memorize_Triangle (A, B, C);
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end if;
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end loop;
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end loop;
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end loop;
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Put_Line (Triangles.Length'Img & " heronian triangles found :");
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Put_Line (Header);
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Triangles.Iterate (Process => Put_Triangle'Access);
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New_Line;
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Put_Line ("Heronian triangles with area = 201");
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Put_Line (Header);
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declare
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Position : Cursor := First_201;
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begin
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loop
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Put_Triangle (Position);
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exit when Position = Last_201;
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Position := Next(Position);
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end loop;
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end;
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end Heronian;
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@ -1,47 +0,0 @@
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function Get-Gcd($a, $b){
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if($a -ge $b){
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$dividend = $a
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$divisor = $b
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}
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else{
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$dividend = $b
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$divisor = $a
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}
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$leftover = 1
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while($leftover -ne 0){
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$leftover = $dividend % $divisor
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if($leftover -ne 0){
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$dividend = $divisor
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$divisor = $leftover
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}
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}
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$divisor
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}
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function Is-Heron($heronArea){
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$heronArea -gt 0 -and $heronArea % 1 -eq 0
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}
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function Get-HeronArea($a, $b, $c){
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$s = ($a + $b + $c) / 2
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[math]::Sqrt($s * ($s - $a) * ($s - $b) * ($s - $c))
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}
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$result = @()
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foreach ($c in 1..200){
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for($b = 1; $b -le $c; $b++){
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for($a = 1; $a -le $b; $a++){
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if((Get-Gcd $c (Get-Gcd $b $a)) -eq 1 -and (Is-Heron(Get-HeronArea $a $b $c))){
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$result += @(,@($a, $b, $c,($a + $b + $c), (Get-HeronArea $a $b $c)))
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}
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}
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}
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}
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$result = $result | sort-object @{Expression={$_[4]}}, @{Expression={$_[3]}}, @{Expression={$_[2]}}
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"Primitive Heronian triangles with sides up to 200: $($result.length)`nFirst ten when ordered by increasing area, then perimeter,then maximum sides:`nSides`t`t`t`tPerimeter`tArea"
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for($i = 0; $i -lt 10; $i++){
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"$($result[$i][0])`t$($result[$i][1])`t$($result[$i][2])`t`t`t$($result[$i][3])`t`t`t$($result[$i][4])"
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}
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"`nArea = 210`nSides`t`t`t`tPerimeter`tArea"
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foreach($i in $result){
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if($i[4] -eq 210){
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"$($i[0])`t$($i[1])`t$($i[2])`t`t`t$($i[3])`t`t`t$($i[4])"
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}
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}
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@ -1,23 +0,0 @@
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Primitive Heronian triangles with sides up to 200: 517
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First ten when ordered by increasing area, then perimeter,then maximum sides:
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Sides Perimeter Area
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3 4 5 12 6
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5 5 6 16 12
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5 5 8 18 12
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4 13 15 32 24
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5 12 13 30 30
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9 10 17 36 36
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3 25 26 54 36
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7 15 20 42 42
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10 13 13 36 60
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8 15 17 40 60
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Area = 210
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Sides Perimeter Area
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17 25 28 70 210
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20 21 29 70 210
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12 35 37 84 210
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17 28 39 84 210
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7 65 68 140 210
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3 148 149 300 210
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